fill the area with random polygons

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jahanzaib ahmad
jahanzaib ahmad 2019-7-4
https://ww2.mathworks.cn/matlabcentral/answers/405186-fill-area-with-random-circles-having-different-diameters
@ Walter Roberson i m trying this way to make polygons packing .generating a random centroid and making a convex polygon and then using scale function i place that polygon at that centroid position .and then generating till the required area percentage condition fullfilled .please guide me for improvement and i want to avoid polyxpoly function i think it make the code slow. 50 percent area is easy but 70 percent takes alot of time ..plus if there is intersection i m reducing the size of the polygon thats again not a good way because i want polygon between two min and max size .
to measure the size of the polygon i m using minboudrect funciton .(attached )
rA=0.5; % 50 percent area
m=1;
N=9;
x=rand; % random centroid x and y
y=rand;
X=rand(N,2);
XX=X(:,1);
XY=X(:,2);
K=convhull(XX,XY);
AB=[XX(K),XY(K)];
polyin = polyshape(AB);
seivesize=[4.75 9.5]; % reuired size of polygon
D=(seivesize(1)+((seivesize(2)-(seivesize(1))).*rand))/100; % random size of polygon
[rx,ry] = minboundrect(AB(:,1),AB(:,2));
side1=sqrt(((rx(1)-rx(2))^2)+(ry(1)-ry(2))^2);
side2=sqrt(((rx(2)-rx(3))^2)+(ry(2)-ry(3))^2);
sizeofpolygons1=min(side1,side2);
FACTOR=D/sizeofpolygons1; % reducing the size of the polygon by factor
poly1 = scale(polyin,FACTOR,[x,y]);
%plot(poly1);
area2=area(poly1);
AC=[poly1.Vertices(:,1),poly1.Vertices(:,2);poly1.Vertices(1,1),poly1.Vertices(1,2)];
A{m}=AC;
rA=rA-area2; Sarea=0;
%m=m+1;
while rA >= area2
chk3=1;
while (chk3)~=0
x=rand;
y=rand;
P=[x,y];
chk2=[];
for i=1:length(A)
AD=A{i};
AD1=polyshape(AD);
chk1=isinterior(AD1,P);
chk2=[chk2,chk1];
end
chk3=any(chk2);
end
N=9;
X=rand(N,2);
XX=X(:,1);
XY=X(:,2);
K=convhull(XX,XY);
AB=[XX(K),XY(K)];
polyin = polyshape(AB);
seivesize=[4.75 9.5];
D=(seivesize(1)+((seivesize(2)-(seivesize(1))).*rand))/100;
[rx,ry] = minboundrect(AB(:,1),AB(:,2));
side1=sqrt(((rx(1)-rx(2))^2)+(ry(1)-ry(2))^2);
side2=sqrt(((rx(2)-rx(3))^2)+(ry(2)-ry(3))^2);
sizeofpolygons1=min(side1,side2);
FACTOR=D/sizeofpolygons1;
poly1 = scale(polyin,FACTOR,[x,y]);
%area1=area(poly1);
AC=[poly1.Vertices(:,1),poly1.Vertices(:,2);poly1.Vertices(1,1),poly1.Vertices(1,2)];
for j=1:length(A)
AF=A{j};
[Cx,Ca] = polyxpoly(AF(:,1), AF(:,2),AC(:,1),AC(:,2));
while ~isempty(Cx)
polyin1 = polyshape(AC);
FACTOR1=.9;
poly1 = scale(polyin1,FACTOR1,[x,y]);
AC=[poly1.Vertices(:,1),poly1.Vertices(:,2);poly1.Vertices(1,1),poly1.Vertices(1,2)];
[Cx,Ca] = polyxpoly(AF(:,1), AF(:,2),AC(:,1),AC(:,2));
end
end
m=m+1;
A{m}=AC;
polyin1 = polyshape(AC);
area2=area( polyin1);
Sarea=Sarea+area2;
rA=rA- area2;
end
axis equal
axis([-0.1 1.1 -0.1 1.1]);
figure(2);
for i =A
plot(i{:}(:,1), i{:}(:,2),'k');
hold on;
enduntitled.jpg

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